Traditionally, the contact between the end-effector and the target is modeled as a parallel spring-damp model, which requires a time-consumed tuning of values of stiffness and damping factor and an extra force sensor fixed on the end-effector. The above drawbacks inspire the application of complementary problem to uniformly describe the unilateral contact for space robot. A dynamical equation of the space robot with unilateral contact is derived, and a numerical method is developed utilizing the Lemke algorithm. By numerical calculation of a planar 3 degree-of-freedom (DOF) manipulator fastened on a 3 DOF floating base, the effectiveness of the dynamical model is verified.